Pulse charging of an electrochemical cell (a.k.a. a battery) has been shown by many to increase the rate of charge acceptance, thus decreasing the time necessary to charge the cell (or battery).
Most pulse charge algorithms use an ad hoc choice of pulses with no consideration for processes occurring in the battery. Even those algorithms where consideration has been given to the electrochemical processes, erroneous assumptions have been made which result in pulses that are not efficient: they are not properly tuned to the timescale of the electrochemistry. For lithium-ion batteries there are several diffusion processes, each with its own time domain. When the battery is charged, each of these processes is occurring simultaneously (described from cathode-to-anode in the cell):
Lithium ions diffuse out of the cathode and enter the electrolyte where they are solvated by one or more solvent molecules. They may also form ion-pairs or ion-aggregates in solution, with each type of species having its own temperature-dependent concentration and mobility (diffusivity) in the electrolyte.
Driven by the electric current, the lithium-containing species in the electrolyte solution diffuse toward the anode where they form an electrochemical double-layer at the boundary between the electrolyte and the Solid Electrolyte Interphase (SEI). Hereafter this layer will be referred to as the “boundary layer.” The SEI is a passivation layer of reacted material at the surface of the anode. [A passivation layer is a protective layer that prevents further reactions that would erode or corrode the an electrode. Passivation layers are often electronically and/or ionically conductive. In this case, the passivation layer protects the anode from “active” reaction with electrolyte.] The SEI is formed during the first few formation cycles of the cell. Most experimental evidence indicates that the SEI is formed by reaction of the electrolyte with the carbon. The SEI is conductive to lithium ions, but lithium-ions are not stored there (as they are in the anode), and as such it is referred to as a solid electrolyte.
Lithium ions shed their paired species (anions and solvent molecules) and enter the SEI where they continue to diffuse toward the carbon. Lithium ions move from the SEI into the carbon where they continue to diffuse and occupy available sites in the carbon. Each of these processes has an associated time constant. Diffusion of the lithium through the solids (carbon, lithiated metal oxide cathode, and SEI) is relatively fast. The processes occurring at and in the boundary layer are the slowest and are referred to as “rate-limiting.”
It is manipulation of this rate-limiting step that will lead to increased rates of charge for a lithium-ion cell (and battery). The processes occurring in a lithium-ion-polymer (a.k.a. lithium-polymer), and a lithium-ion-gel (a.k.a. lithium-ion-polymer-gel) cell are essentially similar and can be assessed and manipulated by the same methods.
The treatment of the processes in the boundary layer (the boundary layer is that volume of the electrolyte, adjacent to the electrode, where the concentration of lithium ions is in flux and can be manipulated) is not mathematically rigorous or phenomenologically detailed, but can be generally determined given the chemistry and chemical reactions that occur.
The two boundary conditions for this treatment are a consideration of the boundary layer with 1) no flux of lithium ions (zero-current condition) and 2) a constant flux (constant-current condition). The intermediate conditions between these two boundary conditions are of particular interest because during the intermediate condition the boundary layer is susceptible to being manipulated. The way these intermediate conditions can be affected is by using instantaneous current pulses or by using sinusoidal waveforms with short rise times.
Fick's Second Law of diffusion governs most time-dependent diffusion problems in electrochemistry. Fick's law is in the form of a differential equation, which implies that it describes what is common to all diffusion problems and not just the characteristics of a particular diffusion problem. Fundamentally, the concentration of a species (in this case, ions in solution and near the boundary layer) is a function of position and timec=f(x,t)
Fick's laws of diffusion are well known to those skilled in the science of batteries and other electrochemical devices.